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Linköping Studies in Science and Technology

Licentiate Thesis No. 1774

Nitride Thin Films for Thermoelectric

Applications:

Synthesis, Characterization and Theoretical

Predictions

Mohammad Amin Gharavi

Thin Film Physics Division,

Department of Physics, Chemistry and Biology (IFM)

Linköping University, SE-581 83 Linköping, Sweden

Linköping 2017

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Thin Film Physics Division,

Department of Physics, Chemistry and Biology (IFM),

Linköping University, SE-581 83 Linköping, Sweden

© Mohammad Amin Gharavi, 2017

ISBN: 978-91-7685-539-3

ISSN: 0280-7971

Printed by LiU-Tryck, Linköping, Sweden, 2017

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In the name of the lord of both wisdom and mind

To nothing sublimer can thought be applied

The lord of whatever is named or assigned

A place, the sustainer of all and the guide

The Persian epic “The Book of Kings”

Abu ʾl-Qasim Ferdowsi Tusi

10th century A.D.

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Abstract

Thermoelectrics is the reversible process which transforms a temperature

gradient across a material into an external voltage through a phenomenon

known as the Seebeck effect. This has resulted in niche applications such

as solid-state cooling for electronic and optoelectronic devices which

exclude the need for a coolant or any moving parts and long-lasting,

maintenance-free radioisotope thermoelectric generators used for deep-

space exploration. However, the high price and low efficiency of

thermoelectric generators have prompted scientists to search for new

materials and/or methods to improve the efficiency of the already existing

ones. Thermoelectric efficiency is governed by the dimensionless figure of

merit 𝑧𝑇, which depends on the electrical conductivity, thermal

conductivity and Seebeck coefficient value of the material and has rarely

surpassed unity.

In order to address these issues, research conducted on early transition

metal nitrides spearheaded by cubic scandium nitride (ScN) thin films

showed promising results with high power factors close to 3000

μWm−1K−2 at 500 °C. In this thesis, rock-salt cubic chromium nitride

(CrN) deposited in the form of thin films by reactive magnetron sputtering

was chosen for its large Seebeck coefficient of approximately -200 μV/K

and low thermal conductivity between 2 and 4 Wm−1K−1. The results

show that CrN in single crystal form has a low electrical resistivity below

1 mΩcm, a Seebeck coefficient value of -230 μV/K and a power factor close to 5000 μWm−1K−2 at room temperature. These promising results

could lead to CrN based thermoelectric modules which are cheaper and

more stable compared to traditional thermoelectric material such as

bismuth telluride (Bi2Te3) and lead telluride (PbTe).

In addition, the project resulting this thesis was prompted to investigate

prospective ternary nitrides equivalent to ScN with (hopefully) better

thermoelectric properties. Scandium nitride has a relatively high thermal

conductivity value (close to 10 Wm−1K−1), resulting in a low 𝑧𝑇. A

hypothetical ternary equivalent to ScN may have a similar electronic band

structure and large power factor, but with a lower thermal conductivity

value leading to better thermoelectric properties. Thus the elements

magnesium, titanium, zirconium and hafnium were chosen for this

purpose. DFT calculations were used to simulate TiMgN2, ZrMgN2 and

HfMgN2. The results show the MeMgN2 stoichiometry to be stable, with

two rivaling crystal structures: trigonal NaCrS2 and monoclinic LiUN2.

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Preface

This thesis is prepared for my Licentiate defense and is a part of my

PhD studies at the Thin Film Physics Division (Energy Materials

Unit) of the Department of Physics, Chemistry and Biology (IFM)

at Linköping University. The aim of this thesis is to synthesize and

study novel nitride semiconducting thin films (i.e., cubic chromium

nitride) and to simulate hypothetical ternary compounds which have

prospective thermoelectric properties.

This research is financially supported by the European Research

Council under the European Community’s Seventh Framework

Programme (FP/2007-2013)/ERC grant agreement no. 335383, the

Swedish Government Strategic Research Area in Materials Science

on Functional Materials at Linköping University (Faculty Grant

SFO-Mat-LiU No. 2009 00971), the Swedish Foundation for

Strategic Research (SSF) through the Future Research Leaders 5

program, and the Swedish Research Council (VR) under project no.

621-2012-4430. Financial support by the Swedish Research Council

(VR) through International Career Grant No. 330-2014-6336 and

Marie Sklodowska Curie Actions, Cofund, Project INCA 600398, is

gratefully acknowledged. Financial support from VR Grant No.

2016-04810 and the Swedish e-Science Research Centre (SeRC) is

also acknowledged. In addition, the Swedish National Infrastructure

for Computing (SNIC) provided access to the necessary

supercomputer resources located at the National Supercomputer

Center (NSC).

During the course of research underlying this thesis, I was enrolled

in Agora Materiae, a multidisciplinary doctoral program at

Linköping University, Sweden.

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List of included papers

Paper I

Microstructure and Thermoelectric Properties of Chromium Nitride

Thin Films

M. A. Gharavi, S. Kerdsongpanya, S. Schmidt, F. Eriksson, N. V. Nong, J. Lu, C. Pallier

and P. Eklund

Manuscript in final preparation

Author’s contribution:

I planned and coordinated the experiments, and performed all of the

depositions. I characterized the samples with SEM and XRD, and

participated in the TEM, AFM and thermoelectric characterization. I

summarized the data and wrote the manuscript.

Paper II

Theoretical Studies on MeMgN2 Superstructures (Me = Ti, Zr, Hf)

M. A. Gharavi, R. Armiento, B. Alling, P. Eklund

Manuscript in final preparation

Author’s contribution:

I was part of the project planning and discussions. I performed the

calculations and wrote the manuscript.

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Acknowledgements

This thesis would have not been realized without the help and guidance I

received from my family, friends and colleagues. Thus I would like to

express my gratitude and many thanks to all of them.

Per Eklund: My supervisor, who gave me the opportunity to expand my

knowledge in physics, train me with new equipment and techniques, and

encouraged my creativity in the lab by granting me this fantastic

opportunity.

Rickard Armiento: My co-supervisor. You were always there when I

needed help, and you introduced me to the DFT universe!

Björn Alling: My co-supervisor. You kick started my theoretical work and

introduced me to its value.

Camille Pallier: My co-supervisor. For her sharp observation in the lab.

Peter Nilsson: My mentor. You give me good advice during our coffee

break conversations.

Per-Olof Holtz: Head of the Agora Materiae graduate school and a dear

friend. I hope you enjoyed your visit to Iran!

Fredrik Eriksson: A great teacher, researcher and friend. You were

always available when I needed your help!

Jun Lu: For the excellent TEM work.

Jörgen Bengtsson: For the excellent AFM work.

Thomas, Rolf and Harri: I am well aware that the division will stop

functioning properly without your efforts! Thank you for your great job!

Also, I would like to thank Reza Yazdi, Javad Jafari, Rahele Meshkian,

Ludvig Landälv, David Engberg, Mahdi Morsali, Mohsen Golabi, Biplab

Paul, Sit Kerdsongpanya, Nina Tureson, Erik Ekström, Arnaud le Febvrier,

Lina Tengdelius, Lida Khajavi and all of my friends at IFM.

And last but not least, I am ever in debt to my parents who cared for me,

my in-laws who trusted me, and my wonderful wife who blessed my life

with success.

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Table of Contents

1. Introduction ....................................................................................... 1

2. Thin film synthesis and characterization ........................................... 5

Diode sputter deposition ........................................................................ 5

Magnetron sputtering ............................................................................ 8

Reactive sputtering .............................................................................. 12

RF sputtering ....................................................................................... 13

3. The microstructural evolution of thin films ..................................... 15

Epitaxial growth .................................................................................. 15

Polycrystalline Thin Films .................................................................. 16

Formation kinetics ............................................................................... 17

4. Thermoelectrics: basics and challenges ........................................... 21

Basics .................................................................................................. 22

TE property optimization .................................................................... 25

5. Theoretical calculations: phase stability and structure prediction ... 29

The Schrödinger equation ................................................................... 29

Density Functional Theory (DFT) ....................................................... 30

Phase stability ...................................................................................... 32

Simulating equivalent ternaries for scandium nitride .......................... 35

6. Concluding remarks and future work .............................................. 37

References ............................................................................................... 39

List of included papers ............................................................................ 41

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1

1. Introduction

Energy efficiency and greenhouse gas reduction stress the need for

alternative sources of power generation. One logical approach would be to

directly harvest waste heat and to transform it into electrical energy. For

this, thermoelectrics can be used. Thermoelectric devices have many

industrial applications such as waste heat recycling produced from internal

combustion engines and power generation for wearable electronics to name

a few. This is due to the Seebeck effect which is the conversion of a thermal

gradient across a device into an external voltage. The opposite operation,

the Peltier effect, induces a thermal gradient when an electric current is

passed through the thermoelectric device. This property can be used for

refrigeration without the need of a coolant.

The heart of thermoelectric research is to enhance device efficiency, which

is done by maximizing the dimensionless figure of merit, 𝑧𝑇:

𝑧𝑇 =𝛼2𝜎

𝜅𝑇 (eq. 1)

where 𝛼 is the Seebeck coefficient, 𝜎 = 1/𝜌 is the electrical conductivity,

𝜅 is the thermal conductivity, and 𝑇 is the absolute temperature. The Carnot

engine efficiency is obtained when 𝑧𝑇 reaches infinity. By maximizing the

power factor (𝛼2𝜎) and minimizing thermal conductivity, the efficiency of

a thermoelectric device will increase. However, today’s thermoelectric

devices have a relatively low 𝑧𝑇 value of approximately unity, as these three

parameters are interdependent. In addition, usage of traditional

thermoelectric material includes other challenging aspects as well. Bi2Te3

and PbTe are well known thermoelectric materials, but the low production

of tellurium plus the use of toxic elements limits them to niche applications.

This includes solid state cooling for specialized optoelectronics devices,

radio isotope thermoelectric generators used for deep space exploration and

prospective military applications.

To go beyond this, new thermoelectric materials can be engineered

according to the phonon glass – electron crystal (PGEC) approach1, i.e.,

designing materials where charge carriers will flow freely as in a crystal,

but the lattice contribution to thermal conductivity is disrupted much like

phonon scattering in glass. Nanostructuring, doping, alloying and synthesis

2

of multilayers and superlattices, can simultaneously decrease thermal

conductivity and electrical resistivity, resulting in higher 𝑧𝑇 values.

Another method to approach the problem of finding novel thermoelectric

material is to utilize first principles calculations by predicting hypothetical

semiconducting ternaries for thermoelectrics. It is assumed that compared

to a binary, equivalent ternaries composed of heavy elements should have a

similar electronic band structure but with a lower thermal conductivity, thus

the crystal structure would be more effective in phonon scattering without

hindering the charge carrier conduction. Such theoretical methods coupled

with modern computers will allow fast simulations of an equivalent ternary

to any known binary semiconductor. By constructing phase diagrams and

choosing any hypothetically stable compound for band structure

calculations, experimentalists can with a much higher degree of confidence

choose appropriate material systems for research.

Interest in the research in this thesis started with cubic scandium nitride

(ScN). It is known that ScN2 has an approximate power factor of 3000

μWm−1K−2, which is high for an early transition metal nitride mainly

known for high temperature hard coating applications. However, its

relatively high thermal conductivity prevents it use as a thermoelectric

material in pure form. Experimental research continued by synthesizing

cubic chromium nitride (CrN) thin films. These thin films are deposited by

reactive magnetron sputtering, which have the benefit of good control over

the crystal quality and phase purity of the films. In addition magnetron

sputtering is also suitable for synthesizing metastable material and

superlattices, allowing a wide range of sample modification and synthesis.

CrN is a well-known hard coating with good high temperature mechanical

and chemical stability. Thermoelectric measurements (discussed in paper I)

have shown Seebeck coefficient values of -230 μV/K. Under-stoichiometric

single crystal CrN films are shown to have a resistivity below 1 mΩcm

resulting in power factors close to 5000 μWm−1K−2 at room temperature.

In addition, CrN has a low thermal conductivity of approximately 2

Wm−1K−1 which is attributed to the localized 3𝑑 orbitals which give the

electrons large effective masses and consequently low thermal conductivity.

The research revolving around this thesis emphasized on two main

characteristics to improve the thermoelectric properties of CrN:

enhancement of crystal quality for maximum electrical conductivity and

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introducing metallic Cr2N phase impurities in the form of nanoinclusions.

In addition, scandium nitride (ScN) was chosen as an appropriate

thermoelectric group three nitride for simulating a hypothetical

semiconducting ternary. By using density functional theory (DFT), it is

possible to predict a hypothetical equivalent ternary composed of group two

alkaline earth and group four early transition metal nitrides. If successful,

such ternaries could be synthesized experimentally and tested for any

potential thermoelectric properties.

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2. Thin film synthesis and characterization

Synthesis of nanostructured materials can be done by many techniques. For

example, synthesis and fabrication by ball milling and electrodeposition

have shown to be suitable for scaling up to the industrial level while being

affordable and easy to handle. On the other hand, versatile methods such as

molecular beam epitaxy and pulsed laser deposition which can prepare

precise samples in 0D, 1D and 2D morphologies are usually more

complicated and expensive, and are suitable for laboratory research. Some

techniques are both cheap enough for industrial scale mass production while

at the same time capable of producing research-quality samples. Sputter

deposition is one of these methods. This section discusses the basics of

sputter deposition and some of the concepts in utilizing the technique.

Diode sputter deposition Sputter deposition was first reported by W. R. Grove3 in the year 1852 but

it took several decades for it to reach much use. The basic concept of sputter

deposition is based on momentum transfer. Similar to a game of pool, a high

energy incident particle will hit the surface of any desired material, ejecting

the source or “target” atoms (figure 1). The ejected particles will be

transported through the deposition chamber and eventually condense on the

substrate. What makes sputtering attractive for research and industry is that

the synthesis procedure is usually done far from thermodynamic

equilibrium, and metastable materials can be synthesized.

The sputtering yield for a specific working gas is defined as the number of

ejected target atoms per incident particle (normally a noble gas ion) which

is usually between 0.1 and 3. The sputtering yield is related to the energy

and incident angle of the bombarding ions, the relative masses of the ions

and target atoms, ambient pressure, and the surface binding energy of the

target atoms4 5.

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Figure 1. Incident ions will collide with the target material and eject the surface atoms. Particle

energy and mass, incident angle and ambient pressure all play key roles in how the target surface

will be affected.

For sputter deposition, a vacuum chamber is required (figure 2). The created

vacuum is needed to remove any residual gases, especially water vapor,

which can deterioration the synthesis process by oxidization. The maximum

vacuum attainable by the system is known as the base pressure. However

sputtering requires a steady flow of the sputtering gas, which will amount

to a constant working gas pressure. A too low working gas pressure will

prevent the plasma from igniting. A too high working gas pressures will

result in more target material to be sputtered for the deposition, but will also

thermalize the sputtered species, losing their energy. As the distance

between the target and substrate is kept at a constant, thermalized particles

will go through a random walk process and the mean free path will be small,

hindering nucleation at the surface. Particles in a working gas pressure of

4.5 mTorr will have a mean free path of approximately 1 cm.

A noble gas is used as the sputtering gas for inertness. As momentum

transfer is most efficient when the mass of the target atoms and the working

gas are similar, argon gas is used for most targets as it is cheap, abundant

and suitable for most materials, although a gas mixture with neon (for light

element sputtering) or krypton (for heavy element sputtering) could be used.

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Figure 2. High vacuum DC magnetron sputtering chamber “Adam”. Base pressure is 2 × 10-7

𝑚𝐵𝑎𝑟. A base pressures at this level would have an approximate particle mean free path of 250 𝑚.

Note the installation of two magnetrons (plus computer controlled shutters) utilizing two separate

targets. Photo by the author.

In order to ionize the argon gas and guide the ions towards the target, an

electric field is utilized with the target material acting as the negative

terminal (the cathode) and the chamber walls acting as the positive terminal

(the anode). A stray free electron is accelerated by the electric field from

the cathode towards the anode. When the electron reaches the first

ionization energy of argon (15.7 eV), a direct hit with an argon atom will

ionize the atom and eject another electron:

𝑒− + 𝐴𝑟 → 𝐴𝑟+ + 2𝑒− (eq. 2)

Eventually, the result will be an avalanche of electrons constantly ionizing

argon gas which themselves will start to feel the electric field and be

attracted towards the cathode. The outcome of a direct impact with the

target surface will be sputtered atoms and secondary electrons. The

sputtered atoms will travel to the substrate and if the distance between the

target and substrate and the mean free path of the atoms are optimized, a

thin film will deposit on the substrate. On the other hand, the secondary

electrons will again enter an “avalanche” process to continuously form

positive argon ions. The discussed mechanism is known as diode sputter

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deposition which utilizes an electric field and a self-sustaining plasma (a

mixture of positive ions, electrons, and neutral atoms) for the deposition

process. The self-sustainability of the plasma can be visually confirmed by

the plasma glow which is the result of the recombination of an argon ion

with an electron, and emitting visible light (figure 3).

Figure 3. Pure argon plasma glow from the HV duel magnetron sputtering system “Adam”. Photo

by the author.

Today, diode sputtering is generally considered obsolete (however, it is still

used for sputtering targets with magnetic properties). A high working

pressure of 100 mTorr is needed for the plasma to remain self-sustaining

(as the probability of an impact between the electron and the argon atom is

low) and these gas pressures greatly decrease the mean free path of the

ejected atoms resulting a very slow deposition rate with a low film

uniformity. The utilization of a magnetron will allow lower working

pressures (approximately 1-10 mTorr) while self-sustaining the plasma.

Magnetron sputtering The magnetron consists of two or more permanent magnets stationed behind

the target with opposite poles sided next to each other and water-cooled to

insure that their temperature will remain below the Curie temperature. The

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generated magnetic field will trap the secondary electrons forcing them to

move in a helical motion along the field lines, increasing the electronic

mean free path near the target (and ionization process of the working gas)

before being absorbed and allowing lesser working pressures for the

deposition process. The physics behind this phenomenon can be described

by the Lorentz force:

𝑭 = 𝑞𝑒 (𝑬 + 𝒗 × 𝑩) = 𝑚𝑒𝒂 (eq. 3)

The electric and magnetic fields will cause a helical motion (figure 4).

Figure 4. The “right hand law” will force the electron to move in circles in presence of a magnetic

field. The spiral movement will increase the mean free path of the electrons.

A sputtering system that includes a magnetron is known as a magnetron

sputtering system (figure 5). The disadvantage of a magnetron sputtering

system is that only a fraction of the target that is located in between the

magnets is sputtered (the target “race track”).

Methods have been devised to reduce waste. Target providers usually

accept and recycle expensive metallic targets for a lower resale price and

industrial scale sputtering systems incorporate revolving cylindrical or very

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large rectangular targets with an optimized magnet configuration for

maximum target utilization.

Figure 5. Schematic diagram of a target installed above a magnetron. Magnetron sputtering has the

disadvantage of etching only a fraction of the target material known as the “race track”. Photo by

the author.

The strength of the magnetic fields of the inner and outer magnets can either

be equal (balanced) or non-equal (unbalanced) which is shown in figure 6.

Balanced magnetrons fully confine the plasma near the target surface while

in the unbalanced configuration magnetic field lines deviate from the center,

covering a larger area. The result will be that the plasma will extend to

include the substrate. The argon ions will affect the growth of the thin film

and can enhance the film quality. Substrate bias is also used in order to

utilize argon ions for the growth process as a negative bias will attract argon

ions towards the growing film. One can regulate the bias voltage and use

this mechanism to ion etch and clean the substrate and remove physisorbed

contaminants or to influence the growing film (adhesion, nucleation, crystal

structure, and texture) by choosing an appropriate bias and form different

film qualities ranging from highly defective polycrystalline films with small

grain sizes to highly textured large grained films. If the bias of the substrate

is positive, electron heating occurs, but typically in a non-uniform and

uncontrollable fashion.

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Figure 6. Magnetrons in the balanced (left) and unbalanced (right) configuration.

The sticking coefficient is temperature dependent. Too low temperatures

will hinder surface diffusion and adatom mobility, which will disrupt the

layer formation. On the other hand, too high temperatures will result in re-

evaporation of different atoms. Decreasing the substrate temperature will

allow deposition on temperature sensitive substrates and will also decrease

the amount of energy required for the process.

Magnetron sputtering systems deposit different materials in both the form

of pure elements and/or solid solutions. For alloys, one can sputter the

desired material from an alloy target. However, the sputtering yield of the

constituents of the alloy target can be an issue. As the sputtering yield for

any given target atom is different, the constituents of the alloy target will

sputter at different rates which may disrupt film stoichiometry. For

example, in a hypothetical AB alloy system, element A may deplete as it

has a higher sputtering yield while a surplus amount of element B will

remain. As time passes equilibrium will form (high sputtering yield for

element A vs. higher concentrations for element B) and stoichiometry will

be preserved leading to the conclusion that alloy sputtering is a self-

sustaining process as long as the target is conditioned initially before

starting the deposition process.

For a compound target (oxide, nitride, etc.) the ejected particles are usually

not of compound nature (metal oxide/nitride molecule). Also the sticking

coefficient of the electronegative element is likely to be lower, resulting

sub-stoichiometric films6. Compounds may have very low sputtering yields

which is why reactive sputtering is used instead.

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Reactive sputtering In reactive sputtering, a reactive gas is included in the gas flow to form

nitrides and oxides (and carbides, oxynitrides, sulfides, etc.). The

molecules/ions of the reactive gas will combine with sputter deposited

atoms and form the compound material. However, the reactive gas may also

react with the target material and “poison” the target by creating an

oxide/nitride film with a new sputtering yield. The deposition process will

continue with a poisoned target, but because the sputtering yield decreases,

the film formation time on the substrate will increase resulting

stoichiometric films but slow depositions. The surface layer may also

increase surface resistivity and the target potential will drop. In order to

solve this problem, the gas flow of the reactive gas must be regulated to

obtain desired deposition rates and stoichiometry. Figure 7 represents a

graph showing the hysteresis loop of the process. The reactive gas flow is

increased to obtain desired stoichiometry, though at the critical point the

target will become poisoned and the deposition rate will drop instantly.

Figure 7. The hysteresis loop for reactive sputtering. Note that the transition from metal target and

compound target takes place at two different gas flows.

Decreasing the gas flow will not instantly exit the system from poisoned

state as it takes time for the reactive gas to desorb from the chamber walls.

An automated feedback loop can be used to maintain the reactive gas flow

in the transition region between poisoned mode and elemental sputtering.

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RF sputtering Another issue regarding sputtering is depositing electrically insulating

materials. As the deposition proceeds and target atoms are ejected,

secondary electrons will form, leaving behind a positive charge on the

target. The accumulation of these charges will disrupt the argon plasma by

repelling the positive ions, decreasing secondary electron formation and

eventually extinguishing the plasma. Also, in order for the target to work at

appreciable currents, very high potentials (1012 V) are required which is not

practical. In this case, we can use radio frequency magnetron sputtering

which utilizes an AC power supply instead of a DC one. The effective

resistance of dielectrics can be varied with the frequency of the electric

current and reasonable voltages can sustain the electric current by seeing a

lower impedance. With the anode and cathode switching signs at a

frequency of 13.56 MHz, the charge build up will be neutralized (self-

biasing) with the electrons preventing the disruption of the plasma. The

heavier ions cannot follow the switching and because the chamber and

substrate are very large, they will not be sputtered in negative bias. One

should note, however, that these power sources are more complex (and

expensive) and because only half the time the target is in negative bias,

deposition rates decrease7.

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3. The microstructural evolution of thin films

The microstructural features of a thin film govern many of the electronic,

optical and mechanical properties. These features include uniformity, grain

size, texture, thickness, etc. Therefore, there is a need for understanding and

control of the microstructural evolution of thin films.

Epitaxial growth Polycrystalline thin films have multiple applications especially as

protective coatings for their desired chemical inertness and/or superior

mechanical properties, but electronic and optoelectronic devices require

epitaxial thin films. This term was first coined in 1928 by Royer8 which is

derived from the Greek words epi (ἐπί), meaning "above", and taxis (τάξις),

meaning "an ordered manner". Depositing a thin film on a monocrystalline

substrate requires the lattice of the film and substrate to match each other

with the least lattice mismatch possible. If coherent heteroepitaxial growth

is desired, strain will ultimately be present but a small lattice mismatch can

be afforded. The strain will increase with film thickness. By the following

equations, on can calculate both the lattice mismatch (𝜖) and critical

thickness (𝑑𝑐) of the film in which the film will be strained but without any

major defects:

𝜖 = (𝑎𝑆 – 𝑎𝐿)/𝑎𝐿 (eq. 4)

𝑑𝑐 ≈ 𝑎𝑆/(2│𝜖│) (eq. 5)

where 𝑎𝑆 is the lattice parameter of the substrate and 𝑎𝐿 is the lattice

parameter of the deposited layer.

In the case where the film thickness exceeds the critical limit (which usually

is the case), relaxation will occur at the film/substrate interface by the

introduction of misfit dislocations. One alternative solution would be to

deposit films of a seed layer on the substrate. The seed layer should have a

low mismatch with the thin film to insure that the relaxation will be

confined to the interface with the substrate.

Thus, the lattice mismatch controls the self-assembly deposition process

which is categorized into three different growth mechanisms (figure 8):

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The Volmer-Weber process: Surface tension is high, adatom-adatom

bonding is preferred, and island growth is distributed across the substrate

surface. The high lattice mismatch and surface roughness of such films

initially make this growth process undesirable for epitaxial films. However,

this process can be very valuable for the synthesis of self-organized zero-

dimensional quantum dots used for optoelectronics9.

The Frank-van der Merwe process: Adatoms tend to bond with the substrate

instead of each other and the stress from lattice mismatch is low, resulting

in a layer by layer growth process of smooth films10 11 12.

The Stranski-Krastanov process: When surface tension and lattice

mismatch is in between the two previous situations, the film will grow in a

layer by layer fashion until reaching the critical thickness. At this point, the

reduction of strain energy will result in island growth. A growth process

like this will result in polycrystalline films if the film thickness exceeds the

critical limit13. This growth mode is also used for self-organized quantum

dot synthesis.

Figure 8. Thin film self-assembly growth mechanisms. Depending on the extent of the lattice

mismatch between the film and the substrate, the film would follow one of the three processes.

Polycrystalline Thin Films The deposited film will arrange itself in a way to obtain maximum stability

and therefore minimum energy. Thus structural evolution is determined by

the minimization of the Gibbs free energy:

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𝐺 = 𝐺0 + ∑ 𝐴𝑖𝛾𝑖 + ∑ 𝐺𝑆𝑗 (eq. 6)

where 𝐴𝑖 is the area of the interface, 𝛾𝑖 is the excess free energy of the

interface and, 𝐺𝑆𝑗 is the energy stored in the strain-inducing defects. 𝐺0 is

the minimum Gibbs free energy of a perfect bulk crystal which is a constant.

𝐴𝑖𝛾𝑖 represents the excess free energy of a crystallite which stems from

grain boundaries (GB), film-substrate interface and film free surface. As a

result, the reduction of ∑ 𝐴𝑖𝛾𝑖 will determine the outcome of the preferred

orientation and grain size. Also, various defects present in the film like

impurity atoms, vacancies, dislocations, stacking faults, etc. will induce

strain inside the film. In order to minimize ∑ 𝐺𝑆𝑗, the growth process will

go towards strain reduction which affects preferred orientation. In cases

where the strain propagates into the film structure, film texture as a function

of film thickness is seen.

Formation kinetics The deposition initially starts by the formation of stable nuclei that come

from impinging atoms on the substrate surface which consequently leads to

stable clusters. The nucleation rate is directly dependent on the deposition

rate and substrate temperature. In the case of sputtering, the deposition rate

depends on the working gas pressure, the target material sputtering yield,

and the energy of the impinging ions. At this point a competition between

various factors emerge. Too high substrate temperatures may cause the

adatoms to re-evaporate from the substrate while too low temperatures will

decrease surface mobility of the adatoms. The ratio of the substrate

temperature over the melting temperature of the deposited material (known

as the homologous temperature, 𝑇𝑠/𝑇𝑚) governs surface diffusion and atom

mobility. In case of high enough mobility, the atoms tend to nucleate around

surface defects and form crystallites with a selected orientation to enhance

stability. Low mobility will result in fine grains or amorphous structures

with a high degree of shadowing effects. In order to increase mobility

without increasing the temperature, a negative substrate bias is a method of

choice in sputtering. The incoming argon ions provide sufficient energy for

grain boundary migration, coalescence, and layer densification. However,

too high energies will result in structural defects inside the film, re-

sputtering and ion implantation, and the incorporation of gas pockets.

18

As the atoms accumulate to form larger and larger nuclei, islands take

shape. Each island has its own unique growth rate and preferred orientation

which stems from minimizing the Gibbs free energy. When the islands grow

large enough, they come into contact (island coalescence). Depending on

the diffusivity and mobility of the atoms, these islands may remain

separated via grain boundaries or some larger islands grow by absorbing

smaller neighboring islands. In low temperature depositions when there is

a small contribution from ion irradiation, the grains tend to be small with

no GB migration. The resulting films will turn porous and polycrystalline

(or even amorphous). The absence of surface diffusion and atom mobility

prevents the system to overcome the activation barrier and the resulting

structures will remain in a metastable state.

In the case of high surface diffusion and atom mobility, the island

coalescence comes to the point in which more energetically favorable

islands will grow at the expense of more unstable ones. In this case, GB

migration and bulk diffusion have a pronounced effect, and recrystallization

occurs. Also, the GB interface energies decrease as grain coarsening

decreases the number of grain boundaries. Islands with a denser set of

planes are more favored; (111) planes for fcc structures, (110) for bcc, and

(0002) for hcp structures14.

In addition to the film deposition process, post growth annealing of the films

can also play a role in altering the microstructure by providing enough

energy for additional GB motion and bulk diffusion leading to a textured

film composed of large crystallites with smooth surfaces.

After a continuous film is developed, film thickening can proceed in

different directions. In case of low mobility situations, incoming atoms will

re-nucleate on the previous grains and atomic shadowing will result a

fibrous film with a high degree of porosity. A structure like this is also

favored when defects and impurities are present, hindering surface

diffusion. In the case of suitable surface diffusion and mobility, localized

epitaxial growth will insure that arriving atoms will continue the crystallite

growth resulting large columnar grains with preferred orientation and

smooth surfaces. Deposition rates also play a role in determining the

microstructure. Too low deposition rates will result an increase in the

impurity inclusion in the film (preventing GB motion, atom mobility and

introducing defects) while too high deposition rates will decrease the

required time for atoms to position themselves for surface diffusion and

19

local epitaxy. The atoms will be “buried” under new incoming atoms and

the film will turn porous.

At this point, a quantitative standard that will relate the main deposition

parameters with the microstructure of the film can be of great importance.

Movchan and Demchishin15 were the first to propose a Structure Zone

Model (SZM) guideline which relates microstructural features to the 𝑇𝑠/𝑇𝑚 ratio (substrate temperature over melting temperature, see figure 9). Other

prominent growth parameters like gas pressure effects and substrate bias

were also taken into account by Thornton16 17 and Messier et al.18 in later

Structure Zone Models.

It is shown that at low 𝑇𝑠/𝑇𝑚, the film will have a fibrous structure,

composed of small crystallites or fully amorphous structures. The incoming

atoms do not have enough kinetic energy to overcome the activation barrier

for atom mobility and surface diffusion. This will result in atomic

shadowing, structural defects, and porosity and the film will be known as a

“zone I” structure.

In case of increased 𝑇𝑠/𝑇𝑚 or with the help of ion irradiation (in which

momentum transport from incoming positive ions to the surface atoms

occur), the film will enter the “transition zone”. The adatoms will now have

enough energy for surface diffusion and GB motion. Zone T thin films are

composed mainly of various crystallites with their respective crystal

orientation engaged in competitive growth. Crystal planes with lower free

energy will prevail and continue to form thin columnar grains with rough

surfaces.

“Zone II” structures form when bulk diffusion is high. At this point liquid

like coalescence is seen and grain coarsening occurs with and after island

coalescence resulting a highly textured film composed of large columnar

grains.

20

Figure 9. Structure zone models for thin films. As the 𝑇𝑠/𝑇𝑚 ratio increases, enhanced adatom

mobility transforms the fibrous and porous film into a dense film composed of large crystal grains.

Drawn based on an original from P.B. Barna and M. Adamik19.

21

4. Thermoelectrics: basics and challenges

The Seebeck effect, which was discovered in the early 1800s, has promise

to address environmental concerns by providing more efficient energy

cycles. Internal combustion engines and industrial facilities produce large

amounts of waste heat which can be recycled to decrease fuel consumption.

This is done by directly transforming a temperature gradient into an

electrical current, a process used for deep-space exploration which requires

reliable and long-lasting power generators. The opposite of the Seebeck

coefficient, the Peltier effect, is used in some consumer applications and has

also drawn interest for its prospective role in providing a reliable and

compact heat spot cooling method for high tech electronic and

optoelectronic devices without the need for a coolant or any moving parts.

Although the proposed applications seem promising, progress in the

development of effective thermoelectric devices has been rather slow. This

is mainly due to the limitations on their efficiency, expressed through the

dimensionless figure of merit zT20:

𝑧𝑇 =𝛼2σ

𝜅𝑇 (eq. 7)

where 𝜎 = 1/𝜌 is the electrical conductivity, 𝛼 is the Seebeck coefficient,

𝑇 is the absolute temperature and 𝜅 is the thermal conductivity of the

material. The product 𝛼2𝜎 is known as the power factor. Note that the

quantity “𝑧𝑇” is preferred over “𝑧”. The reason is that 𝛼2σ

𝜅 changes with

temperature. Thus there is a need for thermoelectric materials for different

temperature regimes. This equation is used to evaluate the performance of

a thermoelectric device. If 𝑧𝑇 reaches infinity, the efficiency of the

thermoelectric device will reach the theoretical maximum of a Carnot heat

engine, but typically the 𝑧𝑇 of modern thermoelectric devices are close to

unity. Unfortunately, the parameters 𝛼, 𝜎 and 𝜅, do not change

independently under ordinary circumstances because of their

interdependence with each other. As a result, the main goal of a materials

scientist would be to maximize the power factor of a thermoelectric device

and minimize its thermal conductivity.

22

Basics If one side of a thermoelectric device is heated and the other side is kept at

a fixed low temperature, an electric current can be measured (figure 10, left

image).

The opposite is also true: if an electric current is passed through a

thermoelectric device, one side will heat up while the other side will start to

cool. This is known as the Peltier effect (figure 10, right image).

Figure 10. Schematic illustration of a thermoelectric couple in power generation (left) and solid-

state refrigeration (right).

The cause is the thermoelectric effect which occurs when a temperature

gradient is established over a conducting or semiconducting material (figure

11). When thermal energy is introduced, the low energy charge carriers

migrate from the hot side of the material to the cold side, causing an electric

field inside the material.

23

Figure 11. When a thermal gradient is established, the more energetic charge carriers (electrons

and holes) with larger mean free paths migrate towards the cold side of the thermoelectric junction

until a stopping electric field is established.

There are a couple of issues that one must take into account regarding

thermoelectrics. Although 𝑧𝑇 gives a good idea of whether a thermoelectric

material has the desired potential, other parameters like device efficiency

must also be considered. First, thermoelectric devices work with material

pairs. Using material with the same charge carrier nature will cancel the

current, as a result n-type and p-type semiconductors are used. A more

applicable equation regarding semiconductor couples is:

𝑧𝑇 =(α𝑝− α𝑛)2𝑇

[(𝜌𝑛 𝜅𝑛)1/2+ (𝜌𝑝 𝜅𝑝)1/2]2 (eq. 8)

The p and n indices represent n-type and p-type semiconductors, which will

form the thermoelectric couple. Note that metals have high thermal

conductivity and very low Seebeck coefficient values and insulators (like

glass) have almost no electrical conductivity, thus the power factor and the

figure of merit of these materials render them useless for thermoelectric

devices unless used in combination with semiconducting material.

If one plans to obtain the efficiency of the device the equation would be:

𝜂𝑇𝐸 =𝑊

𝑄𝐻=

𝑇𝐻− 𝑇𝐶

𝑇𝐻(

(1 +𝑧𝑇𝑀)1/2−1

(1 + 𝑧𝑇𝑀)1/2+ 𝑇𝐶

𝑇𝐻⁄

) (eq. 9)

24

where 𝑇𝑀 is the mean temperature of the device. Based on the above

equation and its relation to the Carnot engine efficiency, at operating

temperatures between 300 and 800 K and a 𝑧𝑇 of 3, one can expect

efficiencies of above 40% of the Carnot efficiency if such 𝑧𝑇 values could

be achieved.

Typical thermoelectric materials are narrow band-gap semiconductors, for

increased electrical conductivity. High electron mobility is also required (𝜇 ≈ 2,000 cm2 (V · s) −1), but the carrier concentration should be

comparatively low so that both the electrical conductivity and the Seebeck

coefficient can be addressed. The following equation explains the

relationship between carrier concentration and the Seebeck coefficient:

𝛼 = 8𝜋2𝑘𝐵

2

3𝑒ℎ2 𝑚∗𝑇(𝜋

3𝑛)2/3 (eq. 10)

A concentration between 1019 and 1020 carriers per 𝑐𝑚3 is considered as an

appropriate amount21 which is material dependent. The previous equation

also shows that the carrier effective mass has a profound effect on the

Seebeck coefficient. The 𝑚∗ refers to the density-of-states effective mass,

which increases with a large slope of the density of states at the Fermi

surface, increasing the Seebeck coefficient. However, a large effective mass

will also decrease electron mobility and consequently, the electrical

conductivity. It can be clearly seen that semiconductors with the required

thermoelectric properties must be carefully selected, tailored and optimized

to reach desired performance.

If the operating temperature of the device is increased, larger band gaps are

needed for thermal conductivity control. High temperatures also cause

diffusion, chemical reactions and contact impairment which can seriously

deteriorate the properties of the device. And as the maximum 𝑧𝑇 value

changes with temperature, no one thermoelectric material can be used for

all applications and thermoelectric materials for different temperature

ranges are required. Traditionally, bismuth telluride (Bi2Te3) for low

temperature, lead telluride (PbTe) for mid-temperature and Si/Ge alloys are

used for high-temperature regimes.

25

However, telluride based thermoelectrics are scarce, expensive and have

thermal, chemical and mechanical stability issues22 23 24. Si/Ge alloys used

for long endurance applications (e.g., the Voyager space program) have

excellent stability, but require very high (~ 1000 °C) temperatures fueled

by expensive 238plutonium oxide for optimal usage.

TE property optimization The main focus on research regarding thermoelectric devices is mainly the

development of semiconductor structures with optimum thermoelectric

properties. For this to be achieved, one must increase the power factor and

decrease the thermal conductivity of each of the semiconductor couples.

The challenging aspect is that these two parameters do not change

independently. In 1995 Slack25 proposed an idea about what are the

characteristics of a good thermoelectric material. He explained that

thermoelectric semiconductors must have the electrical conductivity of a

crystal and the thermal resistivity of glass. This is now known as the Phonon

Glass-Electron Crystal approach (PGEC).

Thermal conductivity stems from charge carrier conduction and lattice

vibrations (phonons). Charge carriers are required for high power factors,

thus research is mainly focused on minimizing thermal conduction by

phonon scattering. The total thermal conductivity is given by the following:

𝜅 = 𝜅 𝑙 + 𝜅𝑒 (eq. 11)

𝜅𝑒 is the electronic contribution of thermal conductivity, and is naturally

tied to the electrical conductivity by the Wiedemann-Franz law:

𝜅𝑒 = 𝐿0𝜎𝑇 (eq. 12)

in which 𝐿0 is the Lorentz number. This relationship and its dependence on

the electrical conductivity 𝜎 shows that not much can be done to decrease

the electronic contribution of thermal conductivity as the power factor will

also decrease.

On the other hand, 𝜅𝑙 is:

𝜅𝑙 =1

3(𝜈𝑆𝐶𝑉𝐿𝑝ℎ) (eq. 13)

26

in which 𝜈𝑆 is the speed of sound, 𝐶𝑉 is the heat capacity at a constant

volume and 𝐿𝑝ℎ is the mean free path of the phonons. At room temperature,

𝜈𝑆 and 𝐶𝑉 are independent of material type, so the main focus would be on

the mean free path of the phonons and methods to decrease it to the point

that it is essentially equal to the interatomic spacing of the constituent

atoms. One such method would be alloying. This would cause short

wavelength acoustic phonon scattering by introducing atomic sized point

defects. An example would be the Si/Ge alloy used for high temperature

radio isotope thermoelectric generators used by NASA. Both of these

materials have a high thermal conductivity but alloying results enhanced

phonon-phonon and phonon-electron scattering26.

Complex inorganic crystals that include heavy metallic atoms also cause

phonon scattering. If voids are created in the lattice structure which are

partially or completely filled with heavy atoms, an effect known as rattling

occurs which can also scatter phonons27. These techniques are used to

reduce the thermal conductivity below the alloy limit28 by scattering mid to

long wavelength phonons. Quantum dots dispersed in a solid matrix can be

formed in a variety of ways, including phase separation of an alloy during

bulk crystal growth or by the Stranski-Krastanov or Volmer-Weber

mechanisms during epitaxial growth. Research has shown that ErAs

nanodots in an InGaAs/InGaAlAs matrix29 will cause effective scattering

with the scattering cross section being proportional to 𝑏6/𝜆4 , where 𝑏 is

the size of the nanodot and 𝜆 is the acoustic phonon wavelength (figure 12).

When these rattlers and quantum dots are unevenly distributed or when the

size varies, the scattering effects increase by reacting with a larger phonon

spectra.

Figure 12. Schematic illustration of various phonon scattering mechanisms in action.

27

Another use of nanotechnology in the development of thermoelectric

devices is the synthesis of superlattices to create charged-carrier

confinement, phonon localization, specular scattering of phonons at

interfaces due to acoustic mismatch and scattering of phonons at defects

(dislocations from lattice mismatch)30 31 32. It has been shown that

superlattice thin films with various/random thicknesses increase the

scattering of phonons at the film interface. Cahill et al. presented

multilayers that have a thermal conductivity comparable with air33

(approximately 0.03 Wm−1K−1). Nanocrystals, polycrystalline structures

and highly disordered thin film crystal layers are also known to decrease the

thermal conductivity. Such procedures will result in a limited flow of hot

electrons which will reduce electrical conductivity, but at high enough

operating temperatures, it will mostly affect the thermal conductivity of the

thermoelectric device and as a result, enhance 𝑧𝑇.

Most modern approaches into maximizing 𝑧𝑇 have been done by decreasing

the lattice contribution of thermal conductivity. It seems that this specific

approach does work well in improving current thermoelectric materials.

However, researching unexpected material is an avenue to be explored.

Semiconducting hard coatings like scandium nitride (ScN) or chromium

nitride (CrN) show good thermal, chemical and mechanical properties at

high temperatures. ScN is known to have high power factors34 (max: 3.3 ×

10-3 Wm−1K−2 at 800 K) and CrN is known to have a Seebeck coefficient

close to -230 μV/K (discussed in paper I) and a thermal conductivity35 36

between 2 and 4 Wm−1K−1. On the negative side, ScN has a relatively high

thermal conductivity37 (8.3 Wm−1K−1), while as CrN has a low electrical

conductivity of approximately 10 mΩcm prompting additional research.

As ScN and CrN are abundant compared to traditional thermoelectric

materials, they can be proposed for synthesis based on the PGEC method

for thermoelectric research.

28

29

5. Theoretical calculations: phase stability and

structure prediction

Modern theoretical methodologies and high speed computers allow

researchers to study and predict the physical and chemical properties of

solids directly from the fundamental equations of quantum mechanics and

thermodynamics38. Experimental research in material science is time

consuming and expensive, thus theoretical calculations can be used to guide

experimentalists and prevent redundant work.

The Schrödinger equation Quantum mechanics provides a theoretical description of the microscopic

world. As most states of matter are composed of positively charged nuclei

surrounded by negatively charged electrons, quantum mechanics is needed

and in principle capable of explaining all material properties. Thus, the

Schrödinger equation is considered a great achievement in physics:

�̂�𝛹 = 𝑖ħ 𝜕𝛹/𝜕𝑡 (eq. 14)

𝛹 = 𝛹 (𝑟1, 𝑟2, 𝑟3, . . . , 𝑅1, 𝑅2, 𝑅3, . . . , 𝑡) (eq. 15)

𝐻 = - 1

2 ∑

ħ2

𝑚𝑒

𝑛𝑖=1 ∇𝑖

2 - 1

2 ∑

ħ2

𝑀𝐼

𝑛𝐼=1 ∇𝐼

2 - ∑𝑍𝐼𝑒2

|𝑟𝑖 − 𝑅𝐼|𝑖,𝐼 + 1

2∑

𝑒2

|𝑟𝑖 − 𝑟𝑗|𝑖≠𝑗 + 1

2∑

𝑍𝐼𝑍𝐽𝑒2

|𝑅𝐼 − 𝑅𝐽|𝐼≠𝐽 (eq. 16)

where equation 14 is the time-dependent Schrödinger equation, equation 15

is the wave function of the quantum system, consisting of 𝑟𝑖 (the coordinates

of the 𝑖𝑡ℎ electron), 𝑅𝐼 (the coordinates of the 𝐼𝑡ℎ nucleus) and 𝑡 (time).

Equation 16 is the Hamiltonian operator. It is needed to describe the energy

state of the wave function and consists of five separate terms: the kinetic

energy of electrons, the kinetic energy of the nuclei, electron-nucleus

attraction, electron-electron repulsion, and nucleus-nucleus repulsion. It

was this equation and other advances in quantum mechanics that prompted

Dirac to announce in 1929 that: “The underlying physical laws necessary

for the mathematical theory of a large part of physics and the whole of

30

chemistry are thus completely known, ...”, but in real macroscopic

materials, 𝑛𝑖 and 𝑁𝐼 are close to 1023 particles, which makes it necessary for

us to simplify the equation otherwise “... the difficulty is only that the exact

application of these laws leads to equations much too complicated to be

soluble”39.

An approximation used to simplify the problem is the Born-Oppenheimer

approximation, where the motion of the electrons and the nuclei are

separated when solving for the electronic degrees of freedom. Second, we

have the Bloch theorem, which states that due to the periodicity of the

crystal lattice, all wave functions must have the same periodicity of the

lattice, making it sufficient to only solve the electronic problem for one unit

cell, and then apply periodic boundary conditions. Although both

modifications greatly simplify the problem at hand, a typical unit cell may

have a hundred electrons which still renders the Schrödinger equation

unsolvable. This is where the electronic density becomes useful.

Density Functional Theory (DFT) Hohenberg and Kohn40 proposed two theorems fundamental to the density

functional theory:

Theorem 1: For any system with interacting particles in an external

potential 𝑉𝑒𝑥𝑡(𝒓), the potential 𝑉𝑒𝑥𝑡(𝒓) is uniquely determined by the

ground state particle density 𝑛0(𝒓) up to an additive constant.

Theorem 2: A universal functional for the energy 𝐸[𝑛, 𝑉𝑒𝑥𝑡] in terms of the

density can be defined, valid for any external potential 𝑉𝑒𝑥𝑡(𝒓). 𝐸0 = 𝐸[𝑛0] is the global energy minima for any particular potential.

In general, instead of determining the allowed energy states by solving the

many-body wave function dependent on 3𝑁 coordinates (𝑁 being the

number of electrons), an electronic density which only depends on 3

coordinates and uniquely defines the ground state properties of the

equivalent many-body system can be used. Any many-body system with an

external potential can be defined by a universal functional of energy.

31

Minimizing this functional will lead to the global energy minimum and

consequently, the ground state properties of the many-body system.

These theorems have the disadvantage that they do not introduce any

universal functional needed to calculate the ground state properties.

However, Kohn and Sham41 proposed a method in which the many-body

electrons is simulated by a fictitious system of non-interacting particles. The

fictitious system is constructed such that the energy of these Kohn-Sham

(KS) particles is minimized by the same density which minimize the energy

of the real electronic system. The Kohn-Sham particle system is described

by:

𝐻𝑒𝑓𝑓𝜓𝑖(𝑟) = [−ħ2

2𝑚𝑒∇2 + 𝑉𝐾𝑆(𝑟)] 𝜓𝑖(𝑟) = 𝜖𝑖𝜓𝑖(𝑟) (eq. 17)

where ħ is the Plank constant, 𝑚𝑒 is the mass of an electron, 𝜓𝑖(𝑟) is the

KS orbitals, 𝜖𝑖 is the KS orbital energy and 𝑉𝐾𝑆 is defined by the Kohn-

Sham approach to the density functional theory:

𝑉𝐾𝑆(𝑟) = 𝑉𝑒𝑥𝑡(𝑟) + ∫𝑛(𝑟´)

|𝑟−𝑟´|𝑑3𝑟´ +

𝛿𝐸𝑥𝑐[𝑛]

𝛿𝑛(𝑟) (eq. 18)

which consists of the electron-nuclei interaction, the internal energy of a

classical repulsive gas, and the electronic quantum effects (the exchange-

correlation term) which stems from non-classical electron repulsion and the

many-body contribution to the kinetic energy. In this equation, 𝑛(𝑟) is a set

of 𝑁 Schrödinger like KS equations and 𝜓𝑖 are the KS orbitals:

𝑛(𝑟) = ∑ |𝜓𝑖(𝑟)|2𝑁𝑖=1 (eq. 19)

Thus, we can simulate real material systems based on the fictitious KS

system and the KS total energy functional:

𝐸[𝑛] = 𝑇[𝑛] + ∫ 𝑉𝑒𝑥𝑡(𝑟)𝑛(𝑟) 𝑑𝑟 +1

2∫ ∫

𝑛(𝑟)𝑛(𝑟´)

|𝑟−𝑟´|𝑑3𝑟𝑑3𝑟´ + 𝐸𝐼𝐼 + 𝐸𝑥𝑐[𝑛] (eq. 20)

where 𝑇[𝑛] is defined as the independent particle kinetic energy and 𝐸𝐼𝐼 is

defined as the interaction between the nuclei. The second term is the energy

from the nuclei or any other external potential and the third term is the

energy of the classical repulsive gas (Hartree term). These results will allow

the calculation of the electronic band structure and phase stability of any

hypothetical crystal.

32

Phase stability A group of atoms can be organized in a crystal structure, thus determining

the electronic properties. However, for a given set of atoms not all crystal

structures are stable. A material system is in thermodynamic equilibrium

when under the conditions of a fixed temperature, pressure and number of

particles, the Gibbs free energy of the material system is at a minimum:

𝐺 = 𝐻 − 𝑇𝑆 (eq. 21)

where 𝐻 is the formation enthalpy, 𝑇 is the absolute temperature and 𝑆 is

the entropy.

The enthalpy 𝐻 is given by

𝐻 = 𝐸 + 𝑃𝑉 (eq. 22)

𝐸 being the total energy of the system, 𝑃 the system pressure and 𝑉 the

system volume. According to the Gibbs free energy equation, the system is

stable when 𝐺 is at a minimum. In the case of an hypothetical binary alloy

composed of element 𝐴 and element 𝐵,

𝛥𝐺𝑚𝑖𝑥(𝑥) = 𝐺 (𝑥) – (𝑥𝐺𝐴 + (1 − 𝑥) 𝐺𝐵) (eq. 23)

where 𝐺 (𝑥) is the free energy of the compound, and 𝐺𝐴 and 𝐺𝐵 are the free

energy of elements 𝐴 and 𝐵 and 𝑥 being the 𝐴 element mass percentage.

Therefore the alloy would be stable compared to the elements if

𝛥𝐺𝑚𝑖𝑥(𝑥) < 0 otherwise it will decompose.

𝛥𝐺𝑚𝑖𝑥(𝑥) can also be expressed by the mixing enthalpy 𝛥𝐻𝑚𝑖𝑥, and mixing

entropy 𝛥𝑆𝑚𝑖𝑥 to produce:

𝛥𝐺𝑚𝑖𝑥 = 𝛥𝐻𝑚𝑖𝑥 − 𝑇𝛥𝑆𝑚𝑖𝑥 (eq. 24)

Figure 13 shows the Gibbs free energy for a hypothetical system consisting

of phase 𝛼 and phase 𝛽, both with a fixed and equal composition. Phase

𝛼 is shown to have a lower Gibbs free energy compared to phase 𝛽,

therefore it is more stable. However, phase transformation requires the

system to overcome the potential barrier 𝑈, causing phase 𝛽 to remain in a

metastable state. Please note that a lower Gibbs free energy will promote

the system to spontaneously undergo transformation, but has nothing to say

on the required time and transformation rates for the process42 which is

studied in chemical kinetics. One well-known example is graphite and

33

diamond, which are both pure carbon. Graphite has a lower Gibbs free

energy compared to diamond and therefore is stable while as the diamond

structure is metastable. However, under standard pressure and temperature

conditions and in practice, “diamonds are forever” as the potential barrier

preventing diamond phase transformation to graphite is very large and

requires time many orders of magnitude longer than the age of the universe.

Figure 13. Hypothetical Gibbs free energy for an atomic arrangement in the form of phase 𝛼 and

phase 𝛽. Phase 𝛼 has a lower Gibbs free energy and is located at the global minimum of the system

compared to phase 𝛽 which is located at a local minimum, therefore phase 𝛼 is stable compared to

the metastable phase 𝛽.

As mentioned previously, DFT calculations are typically performed at a 0

𝐾 temperature. The omitted temperature dependence can affect the Gibbs

free energy, especially for the case of magnetic material, and may change

non-stable phases into stable ones. One good example is chromium nitride

which has an anti-ferromagnetic, orthorhombic structure below 280 K and

transforms into a paramagnetic, face-centered cubic structure at room

temperature43. Also, vibrational energies which are temperature activated

can play a decisive role. However, including temperature is considered a

challenge in first-principle calculations, which requires powerful

computational resources and advanced methods such as the Monte Carlo

technique. Nevertheless, for the case of mixing energies and formation

enthalpies, such effects are often small for the right set of material. For

example, non-magnetic transition metal nitrides which have very high

melting temperatures are decent cases where time consuming temperature-

34

dependent calculations can be avoided in a first round of investigation44 45.

Thus, for phase stability calculations the Gibbs free energy global minimum

used to determine thermodynamic equilibrium mostly depends on the

formation enthalpy of the system:

𝐺 = 𝐻 = 𝐸 + 𝑃𝑉 (eq. 25)

Under normal conditions the pressure (𝑃) is almost zero. In a solid, the

internal energy 𝐸 is composed of a potential energy which originates from

atomic interaction and bonding and will be used for constructing an

enthalpy diagram.

Figure 14 shows a hypothetical binary enthalpy diagram. It is seen that the

formation energy for the compounds are compared to their elemental form.

The lowest energy points are connected to each other by the “convex hull”,

which is defined as a line that encircles all data points without having any

concavities.

To calculate the formation enthalpy per atom (𝐻𝑎𝑡𝑜𝑚) the following

equation is used:

𝐻𝑎𝑡𝑜𝑚 = [𝐸𝑡𝑜𝑡 − 𝑛𝐴(𝐸𝑚𝑖𝑛𝐴 ) − 𝑛𝐵(𝐸𝑚𝑖𝑛

𝐵 )] / 𝑛𝐴+𝐵 (eq. 26)

where 𝐸𝑡𝑜𝑡 is the total energy of the compound phase unit cell, 𝐸𝑚𝑖𝑛 is the

minimum energy of element 𝐴 or 𝐵 and 𝑛 is the total number of atoms of

element 𝐴 or 𝐵 in the unit cell. If 𝐻𝑎𝑡𝑜𝑚 for any given compound is negative

and located on the convex hull, it will be stable, while the remaining data

points located above the hull represent metastable or unstable compounds.

35

Figure 14. Hypothetical enthalpy diagram of elements 𝐴 and 𝐵. The compound mixture in the form

of 𝐴2𝐵 and 𝐴𝐵2 are located on the convex hull and are stable. However the 𝐴𝐵 stoichiometry is not

located on the hull and is either metastable or unstable.

Simulating equivalent ternaries for scandium nitride The aim of conducting theoretical predictions in this thesis is to search for

a possible, as yet hypothetical, replacement for scandium nitride. ScN is a

cubic semiconducting hard coating which has gained interest for

thermoelectrics. It has an approximate power factor of ~3000 μWm−1K−2

at 500 °C which is very high for a transition metal nitride46. In addition to

the power factor, the thermal conductivity of ScN is also high (close to ~10

Wm−1K−1) resulting a low 𝑧𝑇 value and consequently, low thermoelectric

efficiency. While scandium is a reasonably abundant element47, it is

expensive due to modest demand which limits world production. Also,

scandium is an isotopically pure element, which means that phonon

scattering due to isotope impurities is absent.

In a paper published in 2014 by Alling48, it was proposed that one could

search for an equivalent ternary based on ScN. The ternary would have a

similar electronic band structure and Seebeck coefficient, while as the

substituted elements would be better at phonon scattering. An example

would be a naturally layered crystal structure. In his paper, TiMgN2 was

chosen, based on the fact that magnesium and titanium belong to the groups

before (group 2) and after (group 4) scandium in the periodic table. The

results of the research show that not only TiMgN2 is predicted to be stable,

36

but it is also a semiconductor with a 1.1 eV band gap which crystalizes into

the NaCrS2 superstructure (figure 15). This structure can also be described

as a NaCl (B1) based superstructure which includes three alternating layers

of titanium and magnesium. These results open the opportunity to study

other replacements for scandium such as zirconium and hafnium, as both of

these elements are heavier than scandium and titanium. They also consist

of multiple stable isotopes which may enhance phonon scattering. This is

discussed in paper II.

Figure 15. TiMgN2 crystalized into the trigonal NaCrS2 superstructure. Note the alternating layers of titanium and magnesium compared to the smaller nitrogen atoms.

Mg

Ti

Mg

Ti

Mg

Ti

Mg

37

6. Concluding remarks and future work

The results from paper (I) concludes that epitaxial cubic CrN thin films

show good thermoelectric properties with a high power factor close to 5000

μWm−1K−2 at room temperature. The results show that the synthesis

process is sensitive to the gas flow ratio as increasing the nitrogen content

of the gas flow will introduce multiple grain boundaries. This in turn

increases electrical resistivity. On the other hand, decreasing the nitrogen

content will result in the formation of a secondary phase of chromium

nitride: hexagonal Cr2N. Small amounts of Cr2N form in the shape of

randomly dispersed nano-inclusions inside a CrN matrix. The same can also

be said for deposition temperature, as too low deposition temperatures

increase film surface roughness and grain boundaries by limiting surface

diffusion and coalescence while as too high temperatures will cause total

phase transformation from cubic CrN to hexagonal Cr2N. These studies led

to the conclusion that the best thermoelectric properties belong to the phase

pure and single crystal CrN films.

Although the results from paper (I) are promising, the figure of merit for

single crystal CrN thin films is estimated to be 0.5 based on published

thermal conductivity measurements. Chromium is relatively cheap and

abundant, and chromium nitride in comparison with many benchmark

thermoelectric material has superior mechanical, chemical and thermal

stability, but the figure of merit is medium to low. One proposal to enhance

thermoelectric 𝑧𝑇, is to decrease the electric resistivity by doping and

alloying. Elements such as vanadium, tantalum, hafnium and tungsten could

prove suitable as all three form conducting nitrides. Rock-salt cubic

vanadium nitride (VN) has a very similar lattice parameter49 to CrN

(approximately 4.13 Å), making it possible to alloy CrN without disrupting

the single crystal nature of the film. In addition, the synthesis of CrN/(Cr,

V)N superlattices is being studied as a means to reduce thermal conductivity

by introducing quasi-random layer thickness in order to enhance interface

phonon scattering. Rock-salt cubic hafnium nitride (HfN) could also prove

as a suitable candidate when considering the relative atomic mass50 of

hafnium compared to chromium (178.49 vs 51.99). The relatively heavy

elements tantalum and tungsten could potentially form either hexagonal

nanoinclusions (TaN and W2N) or accept the rock-salt cubic structure. In

any case, the effects of adding such elements to CrN could alter the

38

electrical resistivity, thermal conductivity and the Seebeck coefficient

value.

Future research would also require thermal conductivity measurements.

Although the Cr2N nanoinclusions did not show any improvement in the

power factor, studying the effects of these nanoinclusions on the thermal

conductivity is also needed.

In addition to the experimental research, the theoretical studies from paper

(II) showed that TiMgN2, ZrMgN2 and HfMgN2 which were modeled over

cubic scandium nitride all predict stable crystal structures for the given

stoichiometries. These results predict that it is possible to synthesize all

three compounds and to influence the crystal structure by choosing different

substrates as trigonal NaCrS2 and monoclinic LiUN2 both show tendency

for stable crystal structure formation. The band structure calculations also

predicts semiconducting properties which may have prospective

thermoelectric properties better than that of ScN.

Thus, actual laboratory synthesis is needed to determine if TiMgN2,

ZrMgN2 and HfMgN2 exist. Synthesizing these ternaries in either the

trigonal NaCrS2 or the monoclinic LiUN2 structures could be possible by

methods such as DC reactive magnetron sputtering which deposit

compounds far from thermodynamic equilibrium. Actual synthesis would

require a UHV chamber, suitable substrates according to their crystal

structure and lattice parameter (e.g., hexagonal GaN, hexagonal SiC ...) and

the required elemental targets (Mg, Ti, Zr, and Hf). The synthesis of these

ternaries could lead to power factors similar or better than ScN but with

lower thermal conductivities.

39

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41

List of included papers

Microstructure and Thermoelectric Properties of Chromium Nitride

Thin Films

M. A. Gharavi1, S. Kerdsongpanya1, 2, S. Schmidt1, F. Eriksson1, N. V.

Nong3, J. Lu1, C. Pallier1 and P. Eklund1

1 Thin Film Physics Division, Department of Physics, Chemistry and Biology (IFM),

Linköping University, SE-581 83 Linköping, Sweden

2 Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy,

New York, 12180, USA

3 Department of Energy Conversion and Storage, Technical University of Denmark, DK-

4000 Roskilde, Denmark

Manuscript in final preparation

Theoretical Studies on MeMgN2 Superstructures (Me = Ti, Zr, Hf)

M. A. Gharavi1, R. Armiento2, B. Alling1, 3, P. Eklund1

1Thin Film Physics Division, Department of Physics, Chemistry and Biology (IFM),

Linköping University, SE-581 83 Linköping, Sweden

2Theory and Modelling Division, Department of Physics, Chemistry and Biology (IFM),

Linköping University, SE-581 83 Linköping, Sweden

3Max-Planck-Institut für Eisenforschung GmbH, D-40237 Düsseldorf, Germany

Manuscript in final preparation

42

Included Papers

The articles associated with this thesis have been removed for copyright reasons.

For more details about these see:

http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva- 136533